Kramers Nodal Line Metals

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) are Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta (TRIMs). In this work, we show that all achiral non-centrosymmetric materials with SOC belong to a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting TRIMs. The KNLs create Dirac type band touching points at SOC split Fermi surfaces. Due to the touching points, the KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type, the latter of which is particularly interesting. All the states on the octdong Fermi surface are described by two-dimensional massless Dirac Hamiltonians. Therefore, materials with octdong Fermi surfaces support linear optical conductance in the bulk and quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. As an example, we demonstrate how a single Kramers Weyl point can be created near the Fermi energy by straining achiral BiTeI. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they are either KWSs or KNLMs.